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WASHINGTON — A federal judge temporarily has barred the government from publicizing its free credit monitoring offer to veterans whose personal data was stolen and wants to see if they might get a better federal offer.

Lawyers who have filed a class-action lawsuit on behalf of the 26.5 million veterans and active-duty troops affected contend that accepting the government’s offer could jeopardize their chance of winning more money in the privacy suit.

U.S. District Judge William Bertelsman in Kentucky scheduled a hearing this Friday to determine whether the Veterans Affairs Department should revise its offer. His order on the credit monitoring was issued late last Friday.

The suit seeks free monitoring and other credit protection for an indefinite period as well as $1,000 in damages for each person—or up to $26.5 billion total—in what has become one of the nation’s largest information security breaches.

Last week, the department announced its plan to offer free monitoring for a year to millions of veterans and nearly all active-duty military troops whose names, birthdates and Social Security numbers were stolen May 3 from a VA data analyst’s home in suburban Maryland.

The department said it would send out letters to affected veterans and military personnel in early August—after it solicits bids from contractors—on how to sign up for the free service. It also posted information on the government’s Web site.

But in court papers, lawyers for veterans said the VA’s deal was “incomplete and misleading.” The VA must make clear whether veterans who take the government deal will have to give up their rights in court to a potentially larger payout, lawyer Marc Mezibov wrote.

Last week, a Senate committee approved $160 million to pay for the credit monitoring for veterans. It is one of many expected payments as the government struggles with fallout from data breaches crossing at least six agencies.

The VA alone has spent more than $14 million so far to notify veterans by letter and set up a call center, and it is spending an additional $200,000 a day to maintain the call center.